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Dynamic shape is a time series of the outlines of a moving object, which records the temporal variation of the shape of the object during its movement. We believe that the dynamic shape provides clues about the motion performed by the object. In this paper, we borrow tools from system identification to capture the "essence" of the dynamic shape, so that we convert the problems of modelling, learning, and recognizing object motions to the modelling, learning, and comparing of dynamical systems where each motion is represented. Concretely, we use Kenall's definition of shape to represent object contours extracted from each frame, and construct a tangent space with the full Procrustes mean shape as the pole to approximate a linear space for the data set; we then apply these linearized contour representations as training data to learn the dynamical systems, i.e. estimate system parameters; finally supervised pattern classification techniques based on various types of distance measure are adopted for recognition.